Solve for $x$ and $y$ using elimination. ${6x-2y = 2}$ ${-5x+2y = 1}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {6x-2y = 2}\thinspace$ to find $y$ ${6}{(3)}{ - 2y = 2}$ $18-2y = 2$ $18{-18} - 2y = 2{-18}$ $-2y = -16$ $\dfrac{-2y}{{-2}} = \dfrac{-16}{{-2}}$ ${y = 8}$ You can also plug ${x = 3}$ into $\thinspace {-5x+2y = 1}\thinspace$ and get the same answer for $y$ : ${-5}{(3)}{ + 2y = 1}$ ${y = 8}$